1. Field of the Invention
The present invention relates to a method and device for numerical analysis of a flow field of incompressible viscous fluid. This numerical analysis directly uses V-CAD data that have substantial data including shape data and physical quantity data integrated into each other.
2. Description of the Related Art
Patent Literature 1 discloses a method for storing substantial data. In this method, substantial data including shape data and physical quantity data that are integrated into each other can be stored with a small memory. Thereby, it is possible to manage the shape, the structure, the physical property and the history of an object in an integrated fashion. Further, it is possible to manage the data on a series of processes from designing to assembling, testing and evaluating in the same data so that CAD and a simulation can be integrated.
[Patent Literature 1]
Laid-Open Patent Publication No. 2002-230054
As shown in FIG. 1, the method for storing substantial data including integrated shape data and physical property data of Patent Literature 1 includes an external data input step (A1), an oct-tree division step (B1), and a cell data storing step (C1). At the external data input step (A1), external data 12 including boundary data of a target object that is obtained at an external data obtaining step S1 are input to a computer or the like that stores the method. At the oct-tree division step (B1), the external data 12 is divided by oct-tree division into rectangular parallelepiped cells 13 having boundary surfaces orthogonal to each other. At the cell data storing step (C1), various physical property values are stored for each cell.
In the method of Patent Literature 1, the external data having shape data of the object is divided by oct-tree division into rectangular parallelepiped cells having boundary surfaces orthogonal to each other, and various physical property values are stores for each cell. The each divided cells are classified into an internal cell and a boundary cell. The internal cell is positioned inside or outside the target object, and the boundary cell includes the boundary. The internal cell has at least one kind of physical property value as attribute, and the boundary cell has at least two kinds of physical property values for the inside and the outside of the target object.
The data treated in this method is called “V-CAD data”, and a simulation using this data is called “Volume Simulation” or “V-Simulation”. In FIG. 1, the reference numeral 14 designates V-CAD data.
CFD (Computational Fluid Dynamics) has been gradually put into practical use. Accompanying this, grid generation requires more effort and time, and in the case of a complicated shape, the grid generation requires more time than the computation does. For this reason, fluid analysis using an orthogonal grid attracts attention. The fluid analysis using an orthogonal grid is described in Non-Patent Literatures 1 through 17.
The experimental result on a flow around a forcibly oscillated circular cylinder” is described in Non-Patent Literatures 18. Calculation result by an ALE finite element method for self-excited oscillation caused by vortex generation from a circular cylinder is described in Non-Patent Literature 19.
[Non-Patent Literature 1]
Saiki, E. M., Biringen, S., 1996, Numerical Simulation of a Cylinder in Uniform flow: Application of a Virtual Boundary Method, J. Comput. Phys. 123, 450-465.
[Non-Patent Literature 2]
Yabe Takashi et al, 1999, Solid-Liquid-Gas Unification Solving Method and CIP Method, Journal of Japan Society of Computational Fluid Dynamics, 7, 103-114.
[Non-Patent Literature 3]
Ye, T., Mittal, R., Udaykumar, H. S., & Shvy, W., 1999, A Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, AIAA-99-3312, 545-557.
[Non-Patent Literature 4]
Nakano Akira, Shimomura Nobuo, Satobuka Nobuyuki, 1995, Numerical Simulation of compressive Viscous Flows around an Arbitrary Shape Body Using Cartesian Grid System, Transactions of Japan Society of Mechanical Engineers, 61B-592, 4319-4326.
[Non-Patent Literature 5]
Ichikawa Osamu, Fujii Kozo, 2002, Computation of the Flow Field around Arbitrary Three-Dimensional Body Geometry Using Cartesian Grid, Transactions of Japan Society of Mechanical Engineers, 68B-669, 1329-1336.
[Non-Patent Literature 6]
PIAO Binghu, KURODA Shigeaki, 2000, Cartesian grid method for incompressible Viscous Fluid Flow, Journal of Japan Society of Fluid Mechanics, 19, 37-46.
[Non-Patent Literature 7]
Ono, K., Tomita, N., Fujitani, K., & Himeno, R., 1998, An Application of Voxel Modeling Approach to Prediction of Engine Cooling Flow, Society of Automotive Engineers of Japan, Spring Convention, No. 984, 165-168.
[Non-Patent Literature 8]
http://kuwahara.isas.ac.jp/index.html
[Non-Patent Literature 9]
Teramoto Susumu, Fuji Kozo, 1998, Flow Simulation around Three-Dimensional Object Using a Cartesian Grid Method, Proceedings of 12th Computational Fluid Dynamics Symposium, 299-300.
[Non-Patent Literature 10]
Quirk, J. J., 1994, An Alternative to Unstructured Grids for Computing Gas Dynamic Flows Around Arbitrarily Complex Two-Dimensional Bodies, Computers Fluids, 23, 125-142.
[Non-Patent Literature 11]
Karman, S. L. Jr., 1995, SPLITFLOW: A 3D Unstructured Cartesian/Prismatic Grid (12) ynamics of CFD Code for Complex Geome-tries, AIAA 95-0343.
[Non-Patent Literature 12]
Hirt, C. W., & Nichols, B. D., 1981, Volume of Fluid (VOF) Method for the D Free Boundaries, J. Comput. Phys. 39, 201-225.
[Non-Patent Literature 13]
Hirt, C. W., & Cook, J. L., 1972, Calculating Three-dimensional Flows Around Structures and Over Rough Terrain, J. Comput. Phys. 10, 324-340.
[Non-Patent Literature 14]
Kase, Teshima, 2001, Volume CAD Development, Riken Symposium, Integrated Volume CAD System Research, The First Meeting, 6-11.
[Non-Patent Literature 15]
Toyoda, Arakawa, 1999, Analysis of Flow around Circular Cylinder Using Adaptive Cartesian Mesh Method, 13th Computational Fluid Dynamics Symposium, F03-1, CD-ROM,
[Non-Patent Literature 16]
Matsumiya, Koeda, Taniguchi, Kobayashi, 1993, Numerical Simulation of 2D Flow around a Circular Cylinder by Third-Order Upwind Finite Difference Method, Transactions of Japan Society of Mechanical Engineers, 59B-566, 2937-2943.
[Non-Patent Literature 17]
Bouard, R., & Coutanceau, M., 1980, The early stage of development of the wake behind an impulsively started cylinder for 40<Re<10^4, J. Fluid Mech., 101-3, 583-607.
[Non-Patent Literature 18]
Okamoto, S., Uematsu, R., and Taguwa, Y., Fluid force acting on two-dimensional circular cylinder in Lok-in phenomenon, JSME International Journal, B45, No. 4, (2002), 850-856.
[Non-Patent Literature 19]
Kondou, Numerical Simulation for Aerodynamic Behaviors of a Circular Cylinder, 15th Computational Fluid Dynamics Symposium, E09-2, (2001), CD-ROM
At present, in the fluid analysis, calculation of even a complicated flow field having a three-dimensional shape becomes possible by using an overlapped grid and unstructured grid method. However, mesh generation comes to occupy a large part of the entire simulation. For this reason, use of an orthogonal grid is desired for a mesh generation method that enables complete automatization.
In numerical analysis on an arbitrary shape in an orthogonal grid system, it is generally difficult to treat an object boundary. Recently, several Cartesian grid methods have been proposed for discretizations near a fluid boundary, and a boundary condition.
Specifically, there are proposed a virtual boundary of Non-Patent Literature 1, CIP (Cubic-Interpolated Propagation) of Non-Patent Literature 2, an immersed boundary method of Non-Patent Literature 3, NPLS (neighboring Point Local collection) of Non-Patent Literature 4, a method of introducing into a differential scheme a distance from the boundary located between the grid points of Non-Patent Literature 5, and a partial boundary adaptive Cartesian grid method of Non-Patent Literature 6.
In these methods, the boundary of the object is strictly treated. However, to that extent, a computation process become more complicated. Accordingly, these methods are not necessarily suitable to a three-dimensional treatment for an arbitrary shape.
On the other hand, in terms of practical use, two methods are promising. One method of the two forms a stepped boundary by using orthogonal grids so as to approximate an object shape (for example, Non-Patent Literature 7 of Ono in Nissan Automobile, Non-Patent Literature of Kuwabara in Computation Fluid Laboratory. The other method treats a boundary shape by introducing a cut cell to improve approximation (for example, Non-Patent Literature 9 of Fujii in Space Laboratory, Non-Patent Literature 10 of Quirk in J. J., NASA.).
However, in the method using a cut cell, since the boundary extends through an arbitrary position in an orthogonal grid, cells neighboring each other on the boundary can greatly differ in size. For this reason, there is a report that viscous flow analysis is difficult in the cut cell orthogonal grid (refer to Non-Patent Literature 11).
When numerical analysis on a flow field of incompressible viscous fluid is performed by using the conventional overlapped grids and the unstructured grid, grid generation cannot be completely automatized. For this reason, the grid generation occupies a large part of entire simulation time, so that it was difficult to reduce simulation time.
Meanwhile, although numerical analysis on a flow field using an orthogonal grid enables the grid generation to be automatized, it is difficult to express the object boundary by using orthogonal cells. As a result, simulation accuracy becomes low. Particularly in the case of numerical calculation on a flow accompanied by the moving boundary, movement distance of the moving boundary is limited to integer multiples of a mesh that has a constant size, so that the calculation can become unstable.
Furthermore, particularly in the cut cell method, the boundary extends through an arbitrary position in an orthogonal grid, so that the cells neighboring each other on the boundary can differ in size, so that viscous flow analysis was difficult in the cut cell orthogonal grid.